There is a lot at stake as the winning team goes straight into the final to be played in Hyderabad on May 21, while the losing side gets another chance in the second qualifier, to be played on May 19 in Bengaluru.
Mumbai Indians, even after resting six of their regular XI, outplayed the Kolkata Knight Riders in their last league match to secure the top spot.
Going into Tuesday's clash, Mumbai Indians are expected to be back with their tried and tested combination, except a few changes.
Mumbai's batting has clicked big time this season. When the likes of West Indians Lendl Simmons, Kieron Pollard, stumper Parthiv Patel, skipper Rohit Sharma and young Nitish Rana fire in unison, they can destroy any bowling line-up in the world and Pune's will be no exception.
Besides the top order, the all-round duo of Pandya brothers, Krunal and Hardik, are delivering when needed and the hosts will expect them to rise to the big occasion.
Among the changes, the home team can bring in an in-form Ambati Rayadu in place of Nitish Rana to bolster their batting.
In the bowling department, Sri Lankan Lasith Malinga and New Zealand's Mitchell McClenghan are likely to share the new ball before the death over specialist Jasprit Bumrah comes in along with Hardik. Veteran Harbhajan Singh and leg-spinner Karn Sharma can take care of the middle overs.
On the other hand, Pune will desperately miss the services of their costliest buy this season, England's Ben Stokes, who will join his national side ahead of the International Cricket Council (ICC) Champions Trophy, next month.
Stokes has proved his worth this season, both with the bat and ball whenever the situation demanded.
But Smith's side will take a lot of heart from the performance of their bowlers in their last league tie against Kings XI Punjab on Sunday.
Their pacers Jaydev Unadkat (21 wickets), Shardul Thakur (8 wickets) and Dan Christian (9 wickets) have been impressive and regularly taking wickets.
The trio will need to strike once again to restrict Mumbai and also require support from Australian leggie Adam Zampa.
In the batting department, Pune will bank on their top order comprising Rahul Tripathi, Ajinkya Rahane and Smith to give them a platform for Manoj Tiwary and former skipper Mahendra Singh Dhoni to flourish later in the order.
It will be interesting to see who fills in for the loss of Stokes, who could play the long handle besides steaming in regularly at 140 km/hr.
Mumbai Indians: Rohit Sharma (Captain), Lendl Simmons, Mitchel Johnson, Mitchell McClenghan, Nitish Rana, Parthiv Patel (WK), Saurabh Tiwary, Shreyas Gopal, Tim Southee, Lasith Malinga, Krunal Pandya, Keiron Pollard, Ambati Rayudu, Asela Gunaratne, Harbhajan Singh, Hardik Pandya, Jagdish Suchith, Jaspreet Bumrah, Jos Buttler, Karn Sharma and R Vinay Kumar.
Rising Pune Supergiant: Steve Smith (Captain), Mahendra Singh Dhoni (WK), Rahul Tripathi, Ajinkya Rahane, Manoj Tiwary, Dan Christian, Adam Zampa, Shardul Thakur, Ankush Bains, Lockie Ferguson, Jaydev Unadkat, Usman Khawaja, Milind Tandon, Saurabh Kumar, Iswar Pandey, Jaskaran Singh, Deepak Chahar, Rahul Chahar, Rajat Bhatia, Baba Aparajith, Mayank Agarwal, Ankit Sharma, Ashok Dinda